2014-15 Undergraduate Academic Catalog

**MTH 100. ALGEBRAIC CONCEPTS 4 sh**

This course is designed to develop and maintain proficiency in basic algebra skills and to prepare students for future mathematics work in college courses. Topics include exponents, factoring, equation solving, rational expressions, radicals, quadratic equations, graphs of functions, descriptive statistics and regression. A specific graphing calculator is required. This course must be completed with C- or better before taking any other mathematics course. Elective credit only. Offered fall.

**MTH 110. GENERAL STATISTICS 4 sh**

This course provides an introduction to modern statistics. Students will analyze and critically interpret real world data. This course emphasizes written and oral communication, use of technology and collaborative learning. Topics covered include descriptive statistics, basic probability, inferential statistics including one-sample confidence intervals and hypothesis testing and regression analysis. A specific graphing calculator is required. Prerequisite: MTH 100 or placement exemption. Offered fall and spring.

**MTH 116. APPLIED CALCULUS 4 sh**

This introduction to linear systems and differential calculus emphasizes applications to problem solving in business and economics. Students gain enhanced ability to analyze a problem mathematically and study the following topics: functions, limits, derivatives and applications of derivatives. No credit for students with MTH 151 or its exemption. A specific graphing calculator is required. Prerequisite: MTH 100 or placement exemption. Offered fall, winter and spring.

**MTH 151. CALCULUS I 4 sh**

This rigorous first course in single variable calculus builds on knowledge of algebra, trigonometry, and functions. Students are introduced to the computational and theoretical aspects of the study of rates of change and accumulation of functions. Topics include limits and continuity, derivatives and their applications, differentiation rules, antiderivatives, the definite integral, and the fundamental theorem of calculus. A specific graphing calculator is required. Prerequisite: Placement. Offered fall and spring.

**MTH 208. ****Number & Algebra for K-8 Teachers 4 sh**

This course is designed to provide students majoring in elementary education, special education or middle grades education with a deep conceptual knowledge for teaching mathematics. The main focus is the integration of mathematical content with the process standards (problem solving, communication, reasoning, representation and connections within and outside of mathematics). Content includes numeration systems, set theory, number theory, rational and irrational numbers (concepts, operations, properties and algorithms) and algebraic reasoning. Prerequisite: MTH 110 or MTH 151 or higher. Offered fall, winter, and spring of odd-numbered years

**MTH 209. ****Geometry & Data for K-8 Teachers 4 sh**

This course is designed to provide students majoring in elementary education, special education or middle grades education with a deep conceptual knowledge for teaching mathematics. The main focus is the integration of mathematical content with the process standards (problem solving, communication, reasoning, representation and connections within and outside of mathematics). Content includes geometry, measurement and selected topics in probability and statistics. Prerequisite: MTH 110 or MTH 111 or higher. Offered fall, winter, and spring of even-numbered years

**MTH 220 /STS 212. STATISTICS IN APPLICATION 4 sh**

An introduction to concepts in statistics at a deeper quantitative level than that offered in MTH 110. This course emphasizes rationales, applications and interpretations using advanced statistical software. Examples are drawn primarily from economics, education, psychology, sociology, political science, biology and medicine. Topics include introductory design of experiments, data acquisition, graphical exploration and presentation, descriptive statistics, one- and two-sample inferential techniques, simple/multiple regression, goodness of fit and independence and one-way/two-way analysis of variance (ANOVA). Written reports link statistical theory and practice with communication of results. Recommended for students pursuing quantitatively based careers. Prerequisites: MTH 110, MTH 151, placement exemption or permission of the statistics program coordinator. Cross-listed with STS 212. Offered fall and spring.

**MTH 239. LINEAR ALGEBRA 4 sh**

This introductory course in linear algebra includes systems of linear equations, matrices, determinants, vector spaces, eigenvalues, eigenvectors, orthogonality and linear transformations including a variety of applications. Students will begin expanding from a computational focus to a theoretical one by focusing on definitions, considering the proofs of the major theorems, and writing beginning proofs. Corequisite: MTH 251. Offered fall and spring.

**MTH 241. DISCRETE STRUCTURES 4 sh**

This course offers an intensive introduction to discrete mathematics as it is used in computing sciences. Topics include functions, relations, propositional and predicate logic, simple circuit logic, proof techniques and elementary and discrete probability. Prerequisite: MTH 116 or MTH 151 or CSC 130 or currently taking CSC 130. Offered fall.

**MTH 243. APPLIED MATHEMATICAL MODELING 4 sh**

This course is intended to familiarize students with modeling techniques that apply to scientific and industrial situations. Topics discussed may include growth and decay models, the concept of saturable processes, elementary differential equation models, and the use of these models and concepts in various disciplines. Prerequisite: MTH 221. Offered fall.

**MTH 251. CALCULUS II 4 sh**

Students explore applications of the definite integral, differentiation and integration of transcendental functions, techniques of integration, indeterminate forms, improper integrals, infinite sequences and series. Students will be introduced to abstract mathematical thought through formal definitions and proofs. A specific graphing calculator is required. Prerequisite: MTH 151. Offered fall and spring.

**MTH 252. MULTIVARIABLE CALCULUS AND ANALYTIC GEOMETRY 4 sh**

This course provides a study of advanced techniques of differential and integral calculus, including plane curves and polar coordinates, three-dimensional analytic geometry including vectors, differentiation and integration of multivariable functions and applications. A specific graphing calculator is required. Prerequisite: MTH 251. Offered fall and spring.

**MTH 308. MATHEMATICS FOR MIDDLE GRADES AND SECONDARY TEACHERS 4 sh**

The course presents students with mathematics problems, open-ended mathematical investigations, challenges to organize and communicate information from these investigations and the use of technology and manipulative tools to accomplish such tasks. Problems consist of applications of mathematics content from the secondary curriculum. The content includes topics such as relations, functions and their graphs, geometric concepts and proofs, measurement, conics; trigonometry, graph theory, number theory and data analysis and probability. The course also provides a historical context for mathematics problems including the contributions from various cultures. Offered fall of odd-numbered years.

**MTH 309. 21st CENTURY TECHNOLOGY IN MATHEMATICS 1 sh**

This course will expose students to the use of technology in mathematics instruction by examining discipline-specific software as essential tools for 21st century teachers. Topics include numbers and operations, geometry, algebra, data analysis and statistics with a focus on mathematical practices associated with the common core standards. Prerequisite: Admission to the teacher education program.

**MTH 326. THEORY OF COMPUTATION 4 sh**

Cross-listed with CSC 351. See CSC 351 for description.

**MTH 329/STS 341. PROBABILITY THEORY AND STATISTICS 4 sh**

Topics include axiomatic probability, counting principles, discrete and continuous random variables and their distributions, sampling distributions, central limit theorem, confidence intervals and hypothesis testing. Prerequisite: MTH 221. Offered fall of even-numbered years. Cross-listed with STS 341.

**MTH 330. MATHEMATICAL REASONING 4 sh**

This course continues the transition begun in Math 239 – Linear Algebra from computational to theoretical work. A focused study of proof techniques and reasoning skills builds upon the introduction to theorems and proofs in previous classes by developing the reasoning and writing skills necessary to create proofs. Topics include mathematical logic, sets, mathematical induction, combinatorics, relations, and countability arguments. Prerequisite: MTH 239. Offered fall and spring.

**MTH 335. MODERN GEOMETRY 4 sh**

This rigorous treatment of axiomatic foundations of Euclidean geometry through Hilbert’s axioms includes the role and independence of the parallel postulate (revealed through models and neutral geometry), straightedge and compass constructions, historical and philosophical implications of the discovery of non-Euclidean geometry with an introduction to both hyperbolic and elliptic geometry. Prerequisite: MTH 330. Offered fall of odd-numbered years.

**MTH 349. APPLIED MATRIX THEORY 4 sh**

Students are introduced to solutions to systems of linear equations, linear transformations, determinants, vector spaces, orthogonality, matrix algebra, eigenvalues, matrix norms, least squares, singular values, linear programming and approximation techniques. A specific graphing calculator is required. Prerequisite: MTH 241 or MTH 330. Offered spring.

**MTH 359. DIFFERENTIAL EQUATIONS 4 sh**

Topics in this in-depth study of methods of solution and applications of ordinary differential equations include first-order differential equations (linear and nonlinear), linear differential equations of higher order, mathematical models using second-order equations, systems of differential equations and numerical techniques including Euler, Improved Euler and the Runge-Kutta method. Computers or programmable calculators may be used. Prerequisite: MTH 321. Offered spring.

**MTH 371. SPECIAL TOPICS 2-4 sh**

Topics are selected to meet the needs and interests of students.

**MTH 430. ABSTRACT ALGEBRA 4 sh**

Students who have had an introduction to the rules of logic and proof construction are introduced to abstract algebra, including topics such as functions, groups (cyclic, permutation, normal and quotient), properties of groups, rings, fields, homomorphisms, isomorphisms, real and complex numbers and polynomials. Prerequisites: MTH 239 and 330. Offered spring.

**MTH 445. NUMERICAL ANALYSIS 4 sh**

This introduction to numerical analysis includes floating point arithmetic, interpolation, approximation, numerical integration and differentiation, nonlinear equations and linear systems of equations. Prerequisites: CSC 130; MTH 349 or MTH 239; 252; or permission of the instructor. Cross-listed with CSC 415. Offered spring of even-numbered years.

**MTH 455. ANALYSIS 4 sh**

This course provides an in-depth study of topics introduced in the three-course calculus sequence, including sequences and series, continuity and differentiation of functions of a single variable, the Riemann integral and the fundamental theorem of calculus. Prerequisites: MTH 430 and 252. Offered fall.

**MTH/STS 460. SEMINAR I 2 sh**

This course prepares mathematics and statistics majors for Seminar II, the capstone seminar, by instruction and experience in library research and formal oral presentations on advanced mathematical and statistical topics selected by the instructor and students. Prerequisite: Junior/senior standing or permission of the department. Offered spring. Cross-listed with STS 460.

**MTH/STS 461. SEMINAR II 2 sh**

In this capstone experience for senior mathematics and statistics majors, students conduct extensive research on a mathematical or statistical topic and formally present their work in writing and orally. Course requirements may include a satisfactory score on the ETS major field achievement test depending on major. Prerequisite: MTH/STS 460 and junior/senior standing or permission of the department. Offered fall. Cross-listed with STS 461.

**MTH 471. SPECIAL TOPICS 2-4 sh**

Topics are selected to meet the needs and interests of the students.

**MTH 481. INTERNSHIP IN MATHEMATICS 1-4 sh**

The internship provides advanced work experiences in some aspect of mathematical sciences and is offered on an individual basis when suitable opportunities can be arranged. Prerequisite: permission of the department.

**MTH 491. INDEPENDENT STUDY 1-4 sh**

Prerequisite: Permission of the department. May be repeated with different topics for up to a total of eight semester hours.

This page was updated June 30, 2014.